A Characterization of Positive Quadrature Formulae
نویسنده
چکیده
A positive quadrature formula with n nodes which is exact for polynomials of degree In — r — 1, 0 < r < « , is based on the zeros of certain quasi-orthogonal polynomials of degree n . We show that the quasi-orthogonal polynomials that lead to the positive quadrature formulae can all be expressed as characteristic polynomials of a symmetric tridiagonal matrix with positive subdiagonal entries. As a consequence, for a fixed n , every positive quadrature formula is a Gaussian quadrature formula for some nonnegative measure.
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